Hmm, I’m not 100% sure what you mean about multiple accounts. If you mean that you're able to update connection details on FME Flow then the way to check is to have a look into the connection details on FME Flow. You can usually see this in the UI. There might be some connection types where you can’t see this info though.

Which connection type(s) specifically are you looking at?

If it’s an Oauth connection then you most likely will not be able to see the account name as usually FME Server will just store the token. You might have to use an API call to the web service to get the account name of the connection. 

Example: 

Imagine I have a web connection to esri portal on my FME server, this connection could be authorised as user1, user2, user3, serviceaccount1, productionaccount2 etc.

Currently, it seems there is no way to check what account that web connection is currently using as authorisation to connect to esri portal. 

@ecx I’m not aware of any way. With OAuth2.0, which is what most web connections use, the credentials are never stored. They are only used to obtain a token during initial authorization that is used for future authentication. 

What many users will do it put the account name in the web connection name so they know which is which.

I see, this a little disappointing. Occasionally connections get overwritten or authed as another user, which can be hard to debug. Maybe a record of the last user who updated that connection (or authorised it via server) and date would be useful, if that could be added.

As mentioned, not all places will be able to inform you of the user that has authorised. But I do check this on the Esri environment, which does return the username via a call to URL/sharing/rest/portals/self

I have found that very useful over a long time, for the exact issue you mentioned.

Even built myself a custom transformer to do it.